Multipath Nested Gm Nested Miller Compensation

ABSTRACT

A compensated three stage amplifier having high gain as well as high speed is disclosed. The amplifier comprises a NMC and NGCC compensated cascaded three stage amplifier for receiving an input signal and for providing an amplified output signal in dependence thereupon. An extra feed forward transconductance stage extending from the input port of a first gain stage to the output port of a second gain stage of the amplifier is used in order to cancel one of two non-dominant poles in the transfer function of the amplifier with the additional zero introduced by the extra signal path. This results in a transfer function for a three stage cascaded amplifier having only two poles, which is highly desirable by allowing design of such amplifiers providing stable operation at high gain as well as high speed.

FIELD OF THE INVENTION

[0001] This invention relates to the field of multistage amplifiers and,more particularly, to a novel compensation topology for multistageamplifiers having high gain as well as high bandwidth.

BACKGROUND OF THE INVENTION

[0002] High-gain and high-speed amplifiers are vital in modem analogelectronic circuits and are used in a wide range of applications. Theincreasing tendency towards low-voltage designs, especially as manydevices and integrated circuits are made to smaller dimensions, causessignificant problems in amplifier design.

[0003] A particular problem is that as the power supply voltage isscaled down in the design, the threshold voltage does not necessarilyscale down in the same way. For an operational amplifier in such asituation conventional vertical gain enhancement techniques (cascading)are no longer suitable for low-voltage applications and insteadhorizontal gain enhancement techniques (cascading) are employed.Typically, modem cascaded amplifiers comprise three amplifier stages.However, with three cascaded amplifiers the stability of the amplifierand its bandwidth are both limited using existing frequency compensationtechniques.

[0004] To achieve stability at high frequencies in multistageamplifiers, a stabilization topology called Nested Miller Compensation(NMC) was proposed by R. Eschauzier and J. Huijsing, “FrequencyCompensation Techniques for Low Power Operational Amplifiers”, Boston,Mass. Kluwer, (1995). The main drawback of this technique is that theMiller capacitors in the feedback path introduce zeroes in the RightHand complex S-Plane (RHP) degrading stability of the amplifier at highfrequencies. The position in the S-Plane of one of these zeroes isdirectly related to the transconductance of the final stage amplifier.As the transconductance of the final stage amplifier changes due tochanges in the load also the positions of the zeroes with respect tofrequency changes.

[0005] To overcome the drawback of the NMC Fan You and S. H. Embabidisclosed in “Multistage Amplifier Topologies with Nested Gm—CCompensation”, IEEE J. Solid State Circuits, Vol. 32, pp 2000-2011,(1997) the nested Gm—C Compensation (NGCC) topology to cancel out thezeros introduced by the Miller capacitors. However, it is not possibleto use this technique for multistage amplifiers having high gain as wellas high bandwidth, because it only cancels the zeros introduced by theMiller capacitors. For example, in case of a three stage amplifier thetransfer function has three poles, which provide substantialdifficulties in the design of a three stage amplifier having high gainas well as high bandwidth.

[0006] To achieve higher bandwidth a feed forward path has beenintroduced into the existing NMC compensation circuits. The feed forwardpath introduces a zero in the transfer function, which is positionedsuch that it cancels out one of the non-dominant poles in the transferfunction. This topology is known as Multipath Nested Miller Compensation(MNMC) and is disclosed in:

[0007] R. Eschauzier and J. Huijsing, “Frequency Compensation Techniquesfor Low Power Operational Amplifiers”, Boston, Mass. Kluwer, (1995);

[0008] R. Eschauzier, L. Kerklaan, and J. Huij sing, “A 100-MHz 100-dBOperational Amplifier with Multipath Nested Miller CompensationStructure”, IEEE J. Solid-State Circuits, Vol. SC-27, pp. 1709-1717,(1992); and,

[0009] K. Langen, R. Eschauzier, and J. Huij sing, “A 1 GHz Class-ABAmplifier with Multipath Nested Miller Compensation for 76 dB gain”,IEEE J. Solid State Circuits, Vol. SC-32, pp. 488-498, (1997).

[0010] However, this compensation topology also suffers from the samedrawbacks as the NMC topology and does not provide reliable operation ofmultistage amplifiers having high gain as well as high bandwidth.

[0011] It is, therefore, an object of the invention to provide acompensation topology allowing stable operation of high gain, highbandwidth multistage amplifiers. In particular, it is an object of theinvention to provide a compensated three stage amplifier having highgain as well as high bandwidth.

SUMMARY OF THE INVENTION

[0012] In order to overcome the drawbacks of the prior art thecompensation technique according to the invention introduces circuitelements to cancel the zeros introduced by the Miller capacitors as wellas one of the non-dominant poles in the transfer function of a threestage amplifier. The final transfer function of a such compensatedcascaded three stage amplifier has then only two poles. Such a two polesystem is much more desirable for designing a stable cascaded amplifierhaving high gain as well as a wide operating bandwidth, because itsubstantially facilitates the design of a stable operating three stageamplifier.

[0013] According to the invention there is provided a compensated threestage amplifier comprising:

[0014] a first, a second and a third cascaded gain stage for amplifyingan input signal and providing an output signal in dependence thereupon,each gain stage comprising an input port and an output port, wherein theinput signal is received at the input port of the first gain stage andwherein the output signal is provided by the output port of the thirdgain stage;

[0015] a first feedback loop provided from the output port of the thirdgain stage to the output port of the second gain stage;

[0016] a second feedback loop provided from the output port of the thirdgain stage to the output port of the first gain stage;

[0017] a first feed forward transconductance stage extending from theinput port of the first gain stage to the output port of the third gainstage, wherein the first feed forward transconductance stage is forcanceling one of the zeros introduced by the first and second feedbackloop in the transfer function of the three stage amplifier;

[0018] a second feed forward transconductance stage extending from theoutput port of the first gain stage to the output port of the third gainstage, wherein the second feed forward transconductance stage is forcanceling another one of the zeros introduced by the first and secondfeedback loop in the transfer function; and,

[0019] a third feed forward transconductance stage extending from theinput port of the first gain stage to the output port of the second gainstage, wherein the third feed forward transconductance stage is forcanceling one of two non-dominant poles in the transfer functionresulting in a transfer function of the three stage amplifier havingonly two poles.

[0020] According to the invention there is provided a compensated threestage amplifier comprising:

[0021] a NMC and NGCC compensated cascaded three stage amplifier forreceiving an input signal and for providing an amplified output signalin dependence thereupon; and,

[0022] further compensation means, wherein the further compensationmeans is designed such that it cancels one of two non-dominant poles inthe transfer function of the NMC and NGCC compensated cascaded threestage amplifier for providing a transfer function having only two poles.

[0023] According to the invention there is also provided a compensatedthree stage amplifier comprising:

[0024] a NMC and NGCC compensated cascaded three stage amplifier forreceiving an input signal and for providing an amplified output signalin dependence thereupon; and,

[0025] a non-inverting gain stage, wherein the non-inverting gain stageis for canceling one of two non-dominant poles in the transfer functionof the NMC and NGCC compensated cascaded three stage amplifier forproviding a transfer function having only two poles.

[0026] According to the invention there is further provided a method forcompensating a cascaded three stage amplifier comprising the steps of:

[0027] providing a NMC and NGCC compensated cascaded three stageamplifier for receiving an input signal and for providing an amplifiedoutput signal in dependence thereupon;

[0028] providing further compensation means; and,

[0029] using the further compensation means for cancelling anon-dominant pole in the transfer function of the NMC and NGCCcompensated cascaded three stage amplifier in order to provide atransfer function having only two poles.

BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Exemplary embodiments of the invention will now be described inconjunction with the following drawings, in which:

[0031]FIG. 1 is a simplified block diagram schematically illustratingMNMC compensated three stage amplifier according to the prior art—eachsymbol A indicating a Gm stage;

[0032]FIG. 2 is a circuit diagram for small signal analysis of the MNMCcompensated three stage amplifier shown in FIG. 1;

[0033]FIG. 3 is a simplified block diagram schematically illustrating aGm-C compensated two stage amplifier according to the prior art—eachsymbol A indicating a Gm stage;

[0034]FIG. 4 is a simplified block diagram schematically illustrating aMNGCC compensated three stage amplifier according to the presentinvention—each symbol A indicating a Gm stage; and,

[0035]FIG. 5 is a circuit diagram for small signal analysis of the MNGCCcompensated three stage amplifier according to the present inventionshown in FIG. 4.

DETAILED DESCRIPTION OF THE INVENTION

[0036] Amplifiers having high gain and high speed are essentialcomponents in modem analog circuits and are, therefore, widely used in awide range of applications. There is a growing emphasis on designingthese amplifiers using low voltage processes in order to reduce powerconsumption. Furthermore, these amplifiers are employed in deviceshaving smaller dimensions, higher speed and a scaled down supplyvoltage. This causes problems in the amplifier design. To achieve highergain cascading—gain enhancement techniques—are replaced using cascadingof a plurality of amplifier stages. However, cascading of amplifierstages causes severe stability problems.

[0037] Hence frequency compensation techniques are widely used to solvestability problems in multistage amplifiers. One commonly used prior artfrequency compensation technique is the Multi path Nested MillerCompensation (MNMC) technique. FIG. 1 shows a block diagram of a threestage MNMC compensated amplifier. Here, an extra input stage 8 is addedto the Nested Miller Compensation (NMC) circuit. The extra input stage 8introduces a zero in the left hand side of the complex S-domain of thetransfer function of the amplifier. The extra input stage is designedsuch that the introduced zero is placed on top of a non dominant pole ofthe transfer function to cancel its effect. However, Miller capacitors10 and 12 in the feedback paths 11 and 13 introduce zeros in the righthand side of the complex S-domain of the transfer function. The MNMCcompensation technique assumes that the zeros introduced by the Millercapacitors in the S-domain are located at high frequencies and, hence,do not affect the stability of the amplifier at operating frequencies.However, when designing a high speed amplifier for modem analog circuitsthese zeros result in severe stability problems at the higher operatingfrequencies of the modem analog circuits. The zero introduced by theMiller capacitor 10 depends on the transconductance of final stageamplifier 6. As the transconductance of the final stage amplifier 6changes due to changes in the load the zeros move in frequency in theS-domain. This results in a dependence of the stability upon the load ofthe final stage amplifier 6. Referring to FIG. 2 a circuit diagram ofthe MNMC compensated amplifier illustrated in FIG. 1 for small signalanalysis is shown. Based on the circuit diagram shown in FIG. 2 thenodal equations for the transfer function of the MNMC compensatedamplifier are as follows:

(V ₀ −V ₁)sc _(m2) +g _(m3) V ₁ −V ₁(g ₃ +Sc ₁)=0  (1)

(V ₀ −V ₂)sc _(m1) +g _(m2) V ₁ +g _(m6) V _(i) −V ₂(g ₂ +Sc ₂)=0  (2)

(V ₀ −V ₂)sc _(m1)+(V ₀ −V ₁)sc _(m2) +g _(m1) V ₂ +V ₀(g ₁ +Sc₁)=0  (3)

[0038] Rewritten in matrix form equations (1) to (3) result in equation(4): $\begin{matrix}{{\begin{bmatrix}{S\quad C_{m2}} & {- \left( {g_{3} + {S\quad C_{m2}}} \right)} & 0 \\{S\quad C_{m1}} & g_{m2} & {- \left( {g_{2} + {S\quad C_{m1}}} \right)} \\{g_{1} + {S\left( {C_{m1} + C_{m2} + C_{1}} \right)}} & {{- S}\quad C_{m2}} & \left( {g_{m1} - {S\quad C_{m1}}} \right)\end{bmatrix} \cdot \begin{bmatrix}V_{0} \\V_{1} \\V_{2}\end{bmatrix}} = {\quad\begin{bmatrix}{{- g_{m3}}V_{1}} \\{{- g_{m6}}V_{1}} \\0\end{bmatrix}}} & (4)\end{matrix}$

[0039] Based on the following assumptions:

g _(1,2,3)'s<<g _(m1,2,3)'s

C 2, C 3<<C _(m1) , C _(m2) , C _(L)

C ₁ =C _(L)+parasitic capacitance at that node.

[0040] the above matrix is solved using Cramer's rule resulting inequation (5) for the transfer function: $\begin{matrix}{\frac{V\quad o}{V\quad i} = \frac{\begin{matrix}{{{- g_{m1}}g_{m2}g_{m3}} - {S\left\lbrack {{g_{m6}g_{m1}C_{m2}} - {g_{m3}g_{m2}C_{m1}}} \right\rbrack} -} \\{{S^{2}\left\lbrack {{- g_{m6}} - g_{m3}} \right\rbrack}C_{m2}C_{m1}}\end{matrix}}{\begin{matrix}{{g_{1}g_{2}g_{3}} + {S\left\lbrack {g_{m1}g_{m2}C_{m2}} \right\rbrack} +} \\{{{S^{2}\left\lbrack {g_{m1} - g_{m2}} \right\rbrack}C_{m1}C_{m2}} + {S^{3}C_{m1}C_{m2}C_{1}}}\end{matrix}}} & (5)\end{matrix}$

[0041] Solving the quadratic equation in the numerator of equation (5)for S results in a location of two zeros in the complex S-domainintroduced by the Miller capacitors. The zeros act like a pole in thedenominator causing the amplifier to reach instability —open loop gain=1 and phase =180° —within the operating frequency. Therefore, thesezeros need to be compensated.

[0042] To overcome the stability problem caused by the Miller capacitorsfeed forward gain stages have been introduced that drive the Millercapacitors in order to compensate for the zeros introduced by the Millercapacitors. FIG. 3 illustrates this concept for a two stage amplifiercomprising stages 22 and 24. The zero introduced by Miller capacitor 28is compensated by the feed forward gain stage 26. Applying this conceptto a three stage amplifier the resulting Nested Gm-C Compensation (NGCC)circuit removes the zeros introduced by the Miller capacitors.Therefore, the resulting transfer function of the NGCC compensatedamplifier has just 3 poles. On the assumption one of the three polesbeing dominant and the other two being non-dominant, stable operation ofthe amplifier is obtained by spreading the dominant and the non-dominantpoles wide apart in the S-domain. However, balancing a three pole systemis substantially more difficult compared to a two pole system comprisinga dominant pole and a single non-dominant pole. It is, therefore, notstraightforward to design cascaded amplifiers with high gain as well aswide bandwidth.

[0043] This is a serious drawback for the application of cascadedamplifiers in modern analog circuits. In order to meet the requirementsfor these circuits normally three amplifier stages have to be cascaded,resulting in the stability problems outlined above.

[0044] In order to overcome these drawbacks of the prior art thecompensation technique according to the invention introduces means tocancel the zeros introduced by the Miller capacitors as well as one ofthe non-dominant poles in the transfer function of a three stageamplifier in the form of feedback circuit elements and feed forwardtransconductace stages. The final transfer function of such acompensated cascaded three stage amplifier has then only two poles. Sucha two pole system is much more desirable for designing a stable cascadedamplifier having high gain as well as a wide operating bandwidth,because it substantially facilitates the design of a stable operatingthree stage amplifier, as outlined below.

[0045] As will be apparent to those of skill in the art the compensationtechnique according to the invention is not limited to three stageamplifiers but to any number of cascaded amplifiers allowingcancellation of the zeros and a reduction of the number poles in theamplifiers transfer function. However, application of this technique toamplifiers having more than three cascaded amplifiers will result in asystem having more than two poles. For simplicity, the followingdescription of the compensation technique according to the invention islimited to the preferred embodiment of a three stage amplifier.

[0046] Referring to FIG. 4 a Multipath Nested Gm-C Compensation (MNGCC)circuit according to the invention is shown. The MNGCC compensated threestage amplifier 100 according to the invention comprises three amplifierstages 102, 104, and 106, Miller capacitors 110 and 112 providingfeedback loops and feed forward transconductance stages 114 and 116.This topology comprising the three amplifier stages, the Millercapacitors and the feed forward gain stages is comparable to acombination of nested Miller compensation and NGCC. In order to cancelone of the non-dominant poles in the three stage amplifier a parallelpath to the input signal through a feed forward transconductance stage118 is introduced. This additional feed forward transconductance stage118 has same poles as the signal gain stages 102 and 104 and adds a zeroto the transfer function of the amplifier 100. The feed forwardtransconductance stage 118 is designed such that the additional zerocancels one of the non-dominant poles in the transfer function, yieldinga final transfer function with just two poles, which will be shown inthe following.

[0047] Referring to FIG. 5 a circuit diagram of the MNGCC compensatedamplifier 100 according to the invention illustrated in FIG. 4 for smallsignal analysis is shown. Based on the circuit diagram shown in FIG. 5,the nodal equations for the transfer function of the MNGCC compensatedamplifier are as follows:

(V ₀ −V ₁)sc _(m2) +g _(m3) V ₁ −V ₁(g ₃ +Sc ₁)=0  (6)

(V ₀ −V ₂)sc _(m1) +g _(m2) V ₁ +g _(m6) V ₁ −V ₂(g ₂ +Sc ₂)=0  (7)

(V ₀ −V ₂)sc _(m1)+(V ₀ −V ₁)Sc _(m2) +g _(m1) V ₂ +g _(m5) V ₁ +g _(m4)V ₁ +V ₀(g ₁ +Sc ₁)=0  (8)

[0048] Rewritten in matrix form equations (6) to (8) result in equation(9): $\begin{matrix}{{\begin{bmatrix}{S\quad C_{m2}} & {- \left( {g_{3} + {S\quad C_{m2}}} \right)} & 0 \\{S\quad C_{m1}} & g_{m2} & {- \left( {g_{2} + {S\quad C_{m1}}} \right)} \\{g_{1} + {S\left( {C_{m1} + C_{m2} + C_{1}} \right)}} & {g_{m4} - {S\quad C_{m2}}} & \left( {g_{m1} - {S\quad C_{m1}}} \right)\end{bmatrix} \cdot \begin{bmatrix}V_{0} \\V_{1} \\V_{2}\end{bmatrix}} = {\quad\left. \begin{bmatrix}{{- g_{m3}}V_{1}} \\{{- g_{m6}}V_{1}} \\{{- g_{m5}}V_{1}}\end{bmatrix}\rightarrow \right.}} & (9)\end{matrix}$

[0049] Based on the following assumptions:

g _(1,2,3)'s<<g _(m1,2,3)'s

C 2, C 3<<C _(m1) , C _(m2) , C _(L)

C ₁ =C _(L)+parasitic capacitance at that node.

[0050] the above matrix is solved using Cramer's rule resulting inequation (10) for the transfer function: $\begin{matrix}{\frac{V\quad o}{V\quad i} = \frac{\begin{matrix}{{{- g_{m1}}g_{m2}g_{m3}} - {S\left\lbrack {{g_{m4}g_{m3}C_{m1}} + {g_{m6}g_{m1}C_{m2}} -} \right.}} \\{\left. {g_{m3}g_{m2}C_{m1}} \right\rbrack - {{S^{2}\left\lbrack {g_{m5} - g_{m6} - g_{m3}} \right\rbrack}C_{m2}C_{m1}}}\end{matrix}}{\begin{matrix}{{g_{1}g_{2}g_{3}} + {S\left\lbrack {g_{m1}g_{m2}C_{m2}} \right\rbrack} +} \\{{{S^{2}\left\lbrack {g_{m4} + g_{m1} - g_{m2}} \right\rbrack}C_{m1}C_{m2}} + {S^{3}C_{m1}C_{m2}C_{1}}}\end{matrix}}} & (10)\end{matrix}$

[0051] Assuming:

g _(m5) =g _(m3) +g _(m6);

g _(m4) =g _(m2);

[0052] equation (10) is rewritten as follows: $\begin{matrix}{\frac{V\quad o}{V\quad i} = \frac{{{- g_{m1}}g_{m2}g_{m3}} - {S\quad g_{m6}g_{m1}C_{m2}}}{\begin{matrix}{{g_{1}g_{2}g_{3}} + {S\quad g_{m1}g_{m2}C_{m2}} +} \\{{S^{2}g_{m1}C_{m1}C_{m2}} + {S^{3}C_{m1}C_{m2}C_{1}}}\end{matrix}}} & (11)\end{matrix}$

[0053] Taking gm1gm2gm3 common in numerator of equation (11) and g1g2g3common in the denominator of equation (11) by results in equation 12 asfollows:$\frac{V\quad o}{V\quad i} = \frac{{- \frac{g\quad {m1gm2gm3}}{g1g2g3}}\left( {1 + \frac{S\quad g\quad {m6Cm2}}{g\quad {m2gm3}}} \right)}{\begin{matrix}{1 + {S\frac{g\quad {m1gm2gm3Cm2}}{g_{1}g_{2}g_{3}g_{m3}}} + {S^{2}\frac{g\quad {m1gm2gm3Cm2}}{g_{1}g_{2}g_{3}g_{m3}}\frac{C_{m1}}{g_{m2}}} +} \\{S^{3}\frac{g\quad {m1gm2gm3Cm2}}{g_{1}g_{2}g_{3}g_{m3}}\frac{C_{m1}C_{L}}{g_{m2}g_{m1}}}\end{matrix}}$

[0054] Substituting:

C _(m2/gm3) =k ₂;

C _(m1/gm2) =k ₁;

C _(L/gm1)=_(p′1);

A=(gm1gm2gm3)/(g1g2g3);

Zd=(gm2gm3)/(gm6Cm2)

[0055] In equation (12) and simplifying, we get $\begin{matrix}{\frac{V_{o}}{V_{i}} = \frac{A\left( {1 + \frac{S}{Z_{d}}} \right)}{\left( {1 + {S \cdot k_{1}} + {S^{2} \cdot k_{1} \cdot p_{1}^{\prime}}} \right)\left( {1 + {S \cdot A \cdot k_{2}}} \right)}} & (13)\end{matrix}$

[0056] Solving the quadratic equation:1 + S ⋅ k₁ + S² ⋅ k₁ ⋅ p₁^(′) = 0;${S_{1,2} = \frac{{- k_{1}} \pm \sqrt{k_{1}^{2} - {4 \cdot p_{1}^{\prime} \cdot k_{1}}}}{k_{1} \cdot p_{1}^{\prime}}};$

[0057] for S in equation (13) allows the determination of the two polesintroduced by the feed forward gain 118 of the transfer function of theMNGCC compensated amplifier according to the invention: $\begin{matrix}{{{S1} = {\frac{- 1}{2 \cdot p_{1}^{\prime}} \cdot \left\lbrack {1 + \sqrt{1 - \frac{4 \cdot p_{1}^{\prime}}{k_{1}}}} \right\rbrack}};{{S2} = {\frac{- 1}{2 \cdot p_{1}^{\prime}} \cdot \left\lbrack {1 - \sqrt{1 - \frac{4 \cdot p_{1}^{\prime}}{k_{1}}}} \right\rbrack}}} & (14)\end{matrix}$

[0058] Using the MNGCC compensation according to the inventionintroduces a pole S1 being located at a higher frequency while pole S2is located at a lower frequency in the complex S-domain as shown inequation (14). In order to obtain a two pole system for the MNGCCcompensated amplifier pole S2 is placed on zero Zd, so they cancel outeach other.

[0059] This results in a transfer function for the three stage amplifierhaving only two poles—p1′ and S1. Optimizing such a two pole system forhigh gain and high bandwidth is substantially less difficult than athree pole system or a system having two poles and zeros.

[0060] In order to optimize the MNGCC compensated amplifier for highbandwidth the compensation is designed such that pole S1 is located at ahigh frequency in the complex S-domain, preferably as high as possible.However, maximizing S1 in frequency with respect to pole p1′ located ata low frequency in the complex S-domain results in the condition of k1being infinite, which implies the transconductance gm2 being zero, i.e.the MNGCC compensated amplifier is a two stage system. Hence, gain issacrificed for bandwidth. In order to optimize the MNGCC amplifier forhigh gain as well as high bandwidth the compensation is designed suchthat p1′ is approximately 10% of k1. Using these design parametersresults in:${{{S_{1} \approx \frac{- 1}{2 \cdot p_{1}^{\prime}}}\&}\quad \frac{g_{m6}}{C_{m1}}} = {\frac{g_{m3}}{C_{m2}}.}$

[0061] As is evident, choosing p1′ being approximately 10% of k1 hasbeen found by the inventor as a preferred design parameter for specificapplications but is not limited thereto. A person of skill in the artwill be able to determine this parameter according to his or herspecific needs.

[0062] Summarizing the characteristics of the MNGCC compensation circuitaccording to the invention from the above equations reads as follows:${{Dominant}\quad {pole}} = {- \frac{g\quad {m1gm2gm3Cm2}}{g_{1}g_{2}g_{3}g_{m3}}}$${{Non}\text{-}{dominant}\quad {pole}} = {- \frac{g_{m1}}{2C_{L}}}$${{Unity}\quad {Gain}\quad {bandwidth}\quad \left( \omega_{t} \right)} = \frac{g_{m3}}{C_{m2}}$${{Settling}\quad {time}} = \frac{{- \ln}\quad a}{\omega_{t}}$

[0063] The approximate cancellation of a zero and a pole gives rise to apole zero doublet, which causes the settling time to be different fromthat of ordinary 2_(nd) order systems.

[0064] Normalizing the characteristic equations (5) and (11) for MNMCand MNGCC compensated amplifiers, respectively, with respect to gainbandwidth GB allows comparisons of power consumption and bandwidth ofthe two compensation techniques. The normalized equations (15) and (16)for MNMC and MNGCC compensated amplifiers, respectively, read asfollows: $\begin{matrix}{1 + \frac{S\quad {n\left( {G\quad B^{\prime}} \right)}g\quad {m1}^{\prime}g\quad {m2}^{\prime}C\quad {m2}}{g1g2g3} + \frac{S\quad {n^{2}\left( {G\quad B^{\prime}} \right)}^{2}\left( {{g\quad {m1}^{\prime}} - {g\quad {m2}^{\prime}}} \right)C\quad {m2Cm1}}{g1g2g3} + \frac{S\quad {n^{3}\left( {G\quad B^{\prime}} \right)}^{3}C\quad {m2Cm1C1}}{g1g2g3}} & (15) \\{1 + \frac{S\quad {n\left( {G\quad B} \right)}g\quad {m1g}\quad {m2C}\quad {m2}}{g1g2g3} + \frac{S\quad {n^{2}\left( {G\quad B} \right)}^{2}g\quad {m1C}\quad {m2Cm1}}{g1g2g3} + \frac{S\quad {n^{3}\left( {G\quad B} \right)}^{3}C\quad {m2Cm1C1}}{g1g2g3}} & (16)\end{matrix}$

[0065] Assuming a same gain bandwidth GB=GB′ for both compensationtechniques and in equations (15) and (16):

gm1=(gm1'−gm2');

gm1<gm1'

[0066] result in I1<I1′, i.e. for a same gain bandwidth using the MNGCCcompensation technique according to the invention the dissipatedpower—loss—is substantially smaller.

[0067] Therefore, the MNGCC compensation circuit according to theinvention is highly advantageous for implementation in modem analogcircuits by providing a higher bandwidth for multistage amplifiers aswell as reducing the dissipated power which is becoming more and more aconcern if the devices are smaller. This reduces considerably the supplypower and, furthermore, reduces design constrains for providing coolingof smaller devices due to the dissipated power.

[0068] These characteristics make the MNGCC compensated amplifier highlydesirable in many modern applications such as small signal amplifiers asused, for example, in cell phones, and in wireless LANs. Otherapplications of the MNGCC compensated amplifier include use as aterminated cable driver or as a central office driver in X-DSLapplications.

[0069] Numerous other embodiments may be envisaged without departingfrom the spirit or scope of the invention.

What is claimed is:
 1. A compensated three stage amplifier comprising: afirst, a second and a third cascaded gain stage for amplifying an inputsignal and providing an output signal in dependence thereupon, each gainstage comprising an input port and an output port, wherein the inputsignal is received at the input port of the first gain stage and whereinthe output signal is provided by the output port of the third gainstage; a first feedback loop provided from the output port of the thirdgain stage to the output port of the second gain stage; a secondfeedback loop provided from the output port of the third gain stage tothe output port of the first gain stage; a first feed forwardtransconductance stage extending from the input port of the first gainstage to the output port of the third gain stage, wherein the first feedforward transconductance stage is for canceling one of the zerosintroduced by the first and second feedback loop in the transferfunction of the three stage amplifier; a second feed forwardtransconductance stage extending from the output port of the first gainstage to the output port of the third gain stage, wherein the secondfeed forward transconductance stage is for canceling another one of thezeros introduced by the first and second feedback loop in the transferfunction; and, a third feed forward transconductance stage extendingfrom the input port of the first gain stage to the output port of thesecond gain stage, wherein the third feed forward transconductance stageis for canceling one of two non-dominant poles in the transfer functionresulting in a transfer function of the three stage amplifier havingonly two poles.
 2. A compensated three stage amplifier as defined inclaim 1, wherein the first and second gain stage comprises anon-inverting gain stage, and wherein the third gain stage comprises aninverting gain stage.
 3. A compensated three stage amplifier as definedin claim 2, wherein each of the first and the second feed forwardtransconductance stages comprises an inverting gain stage.
 4. Acompensated three stage amplifier as defined in claim 3, wherein thethird feed forward transconductance stage comprises a non-inverting gainstage.
 5. A compensated three stage amplifier comprising: a NMC and NGCCcompensated cascaded three stage amplifier for receiving an input signaland for providing an amplified output signal in dependence thereupon;and, further compensation means, wherein the further compensation meansis for canceling one of two non-dominant poles in the transfer functionof the NMC and NGCC compensated cascaded three stage amplifier forproviding a transfer function having only two poles.
 6. A compensatedthree stage amplifier comprising: a NMC and NGCC compensated cascadedthree stage amplifier for receiving an input signal and for providing anamplified output signal in dependence thereupon; and, a non-invertinggain stage, wherein the non-inverting gain stage is for canceling one oftwo non-dominant poles in the transfer function of the NMC and NGCCcompensated cascaded three stage amplifier for providing a transferfunction having only two poles.
 7. A method for compensating a cascadedthree stage amplifier comprising the steps of: providing a NMC and NGCCcompensated cascaded three stage amplifier for receiving an input signaland for providing an amplified output signal in dependence thereupon;providing further compensation means; and, using the furthercompensation means for cancelling a non-dominant pole in the transferfunction of the NMC and NGCC compensated cascaded three stage amplifierin order to provide a transfer function having only two poles.
 8. Amethod for compensating a cascaded three stage amplifier comprising thesteps of: providing a NMC and NGCC compensated cascaded three stageamplifier for receiving an input signal and for providing an amplifiedoutput signal in dependence thereupon; providing a feed forwardtransconductance stage extending from an input port of a first signalgain stage to an output port of a second signal gain stage; and, usingthe feed forward transconductance stage for cancelling a non-dominantpole in the transfer function of the NMC and NGCC compensated cascadedthree stage amplifier in order to provide a transfer function havingonly two poles.
 9. A method for compensating a cascaded three stageamplifier as defined in claim 8, wherein the feed forwardtransconductance stage comprises a non-inverting gain stage.
 10. Amethod for compensating a cascaded three stage amplifier as defined inclaim 9, wherein the feed forward transconductance stage has same polesas the signal path comprising first and second gain stage.
 11. A methodfor compensating a cascaded three stage amplifier as defined in claim10, wherein a zero introduced by the feed forward transconductance stagecancels one of the non-dominant poles in the transfer function of theNMC and NGCC compensated cascaded three stage amplifier.
 12. A methodfor compensating a cascaded three stage amplifier as defined in claim11, wherein a zero introduced by the feed forward transconductance stagecancels one of the non-dominant poles in the transfer function of theNMC and NGCC compensated cascaded three stage amplifier providing a twopole system for the transfer function having one dominant pole and onenon-dominant pole.
 13. A method for compensating a cascaded three stageamplifier as defined in claim 12, wherein the remaining non-dominantpole is located at a substantially high frequency in the complexS-domain of the transfer function.
 14. A method for compensating acascaded three stage amplifier as defined in claim 13, wherein thedominant pole is determined as being 10% of the ratio of thetransconductance of a feedback loop extending from an output port of thethird signal gain stage to an input port of the third signal gain stageto the transconductance of the second signal gain stage.